There are six different models that are to appear in a fashion show.

Take the task of arranging the models and break it into stages.

Stage 1: Select a model to stand in position #1
There are 6 models to choose from, so we can accomplish this stage in 6 ways.

Stage 2: Select a model to stand in position #2
Since models from the same country must stand together, there's only 1 model who can stand in position #2
So, we can complete this stage in 1 way

Stage 3: Select a model to stand in position #3
There are 4 models remaining, so we can accomplish this stage in 4 ways.

Stage 4: Select a model to stand in position #4
Since models from the same country must stand together, there's only 1 way to complete this stage

Stage 5: Select a model to stand in position #5
There are 2 models remaining, so we can accomplish this stage in 2 ways.

Stage 6: Select a model to stand in position #6
There is only 1 model remaining, so we can accomplish this stage in 1 way.

By the Fundamental Counting Principle (FCP) we can complete all 6 stages (and thus arrange all 6 models) in (6)(1)(4)(1)(2)(1) ways (= 48 ways)

Answer: B

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

RELATED VIDEOS

Let's say that Models of Europe are represented by E1 and E2 respectively

Let's say that Models of South America are represented by S1 and S2

Let's say that Models of North America are represented by Na and N2

So we have to define the total ways of entries of E1 E2 S1 S2 N1 N2

We have to keep E1 E2 together and similarly N1 N2 together and similarly S1 S2 together so make three groups of two models from same region each

Arrangement of these three Group can be done in 3! ways

Arrangement of Models within Group can be done in 2!x2!x2! ways

i.e. Total Ways of Arranging the models so that they are grouped as per region together = (3!)*(2!x2!x2!) = 6*8 = 48

Answer: Option B

Three groups can be arranged way= 3!..
within each group the two models can be arranged in 2! ways ..
total ways 3!*2!*2!*2!=48
ans B

The highlighted part has calculation mistake 3!*3*2! = 36

I hope it's just a typo error.

Out of 6 positions, 3 continents can be arranged in 3! Ways=6
Out of those 3 continents each 2 model can be arranged in 2!*2!*2! Ways= 8
So total number of arrangements for models to be arranged for 6 places =6*8=48

Hence answer is B

Thanks,

Platinum GMAT Official Solution:

In this problem, order is important. Jane standing to the left of Mary is a different arrangement than Mary standing to the left of Jane. Because order is important, the permutations equation is used.

The formula for a permutation is:
nPr= n!/(n-r)!
where n is the total number of selections available and r is the number of items to be selected.

For each set of two models from each continent, there are 2P2ways to arrange them. From the permutation formula with n equal to 2 and r equal to 2 this results in:
2P2= 2! = 2

Since there three groups of two there are:
2P2*2P2*2P2 or 2*2*2 or 8 ways to arrange each group within each group.

Since there are three groups of models that can be placed in three different positions there are:
3P3ways to arrange the three groups.

The value of 3P3is (3*2*1)/(3-3)! = 6/0! = 6, or 6 ways to arrange the different groups. Note that 0! is defined to be equal to one.

Since there are 6 ways to arrange the groups and 8 ways to arrange the models within their own groups there are:
8X6 or 48 different ways to arrange the models.

So the correct answer is B.

Hi Bunuel,

In your solution it says option A as the answer, must be a typo. Just to let you know.

Thanks.

Edited the typo. Thank you for noticing it.

2! X 2! X 2! X 3! = 48. (B)

Since Models will sit in pair, So virtually we have 3 place and 3 Pairs to Sit. So three pair can take seat in 3*2 * 1 ways,
Each pair has 2 combination so (2*2*2) inter changeable combination within the pair.

So total combination = 3*2*1 * 2*2*2 = 48

Hence Option B should be correct.

3!*2!*2!*2! equals to 48

Sent from my SM-J200H using GMAT Club Forum mobile app

i foolishly just calculated the model arrangement = 8. nice explaination. thank you

Hey guys, maybe the wording of the question should be revised. North America and South America are part of the SAME continent, America. With the current wording, the answer should be 72.

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.